This value is considerably less than that obtained for pure adiabatic operation (19.7 tons). The heat losses tend to partially remove thermodynamic constraints on the reaction rate and permit a closer approach to the optimum temperature profile corresponding to minimum catalyst requirements. [Pg.519]

An explicit example of an equilibrium ensemble is the microcanonical ensemble, which describes closed systems with adiabatic walls. Such systems have constraints of fixed N, V and E < W< E + E. E is very small compared to E, and corresponds to the assumed very weak interaction of the isolated system with the surroundings. E has to be chosen such that it is larger than (Si ) [Pg.386]

Since the only constraint we have placed on Qi is that it be less than 9, the second isotherm can be as arbitrarily close to the first as we wish. The conclusion that states exist on this second isotherm that cannot be reached from a point on the first isotherm by any adiabatic path is therefore general. Thus, we can argue that there are states located in the plane defined by 6 and xi that are inaccessible from state 1. [Pg.70]

In most bench-scale reaction instruments, it is also possible to perform adiabatic experiments, although precautions have to be taken to avoid an uncontrollable runaway in the final stages. From these types of experiments, the temperature constraints at which, for example, side reactions or decomposition reactions start, together with the possible control requirements, can be obtained. If the adiabatic temperature rise may exceed, say, 50 to 100°C, it is safer to use other methods to obtain similar information, such as the DSC, ARC, or Sikarex, because these instruments use relatively small amounts, thereby decreasing the potential hazard of an uncontrollable runaway event in the test equipment. [Pg.133]

Figure 1. Semilogarithmic presentation of species profiles for thermal decomposition of N2O starting at P = 1 atm and T = 1500 K under constant-density, adiabatic constraints. The concentration of N2O4 is off scale. (See Fig. 2.) |

Chaiken (Ref 28) has shown that the cavitation model is consistent with the classical C-J picture of detonation, provided that additional constraints, due to the several rate processes that take place in LVD, are imposed on the classical treatment. In essence, he has shown that not all Hugoniot adiabatic states can be accessible from a given initial state, if the precursor shock acts to couple rate processes ahead of the reaction shock front with rate processes behind this front. The solution of the Rankine-Hugoniot (classical detonation). [Pg.588]

In Eq. (9-62) MjL is the mass of atom //. The mass mq does not correspond to any physical mass and is simply set to a value small enough such that the charges follow the atomic coordinates adiabatically. The Lagrangian also includes an Nmoiec number of constraints to ensure that each molecule remains electrostatically neutral. [Pg.242]

The above are obvious generalizations of Eqs. (1.13.5)-(1.13.8), which, incidentally, justifies the adoption of Eq. (1.20.1a). As before, the most useful formulations are the ones that specify S and P. Also, E and H are the appropriate functions of state under adiabatic constraints, whereas A and G are appropriate for characterizing isothermal processes. [Pg.94]

Here, Tj is the inlet temperature to the system, which is specified at Ty, = 290 K for the current problem. The expression for T, given by Equation 7.13, may be substituted into Equation 7.12 and the rate expressions. The resulting rate field after substitution now incorporates the adiabatic constraint imposed on the system, and it is necessarily different compared to an equivalent isothermal system. [Pg.206]

In the formulation of the boundary conditions, it is presumed that there is no dispersion in the feed line and that the entering fluid is uniform in temperature and composition. In addition to the above boundary conditions, it is also necessary to formulate appropriate equations to express the energy transfer constraints imposed on the system (e.g., adiabatic, isothermal, or nonisothermal-nonadiabatic operation). For the one-dimensional models, boundary conditions 12.7.34 and 12.7.35 hold for all R, and not just at R = 0. [Pg.505]

AR Construction Since the reactor temperature has been expressed explicitly in terms of components x and y, construction of the AR for the adiabatic system from this point onward follows the same approach as that for an isothermal system. The system is two-dimensional as there are two independent reactions participating in the system, and therefore we need only consider combinations of PFRs and CSTRs in the construction of the candidate region. It is customary to begin by generating the PER trajectory and CSTR locus from the feed. Due to the nonlinear nature of the kinetics introduced by the adiabatic constraint, the system exhibits multiple CSTR solutions from the feed point. We [Pg.206]

One of the simplest calorimetric methods is combustion bomb calorimetry . In essence this involves the direct reaction of a sample material and a gas, such as O or F, within a sealed container and the measurement of the heat which is produced by the reaction. As the heat involved can be very large, and the rate of reaction very fast, the reaction may be explosive, hence the term combustion bomb . The calorimeter must be calibrated so that heat absorbed by the calorimeter is well characterised and the heat necessary to initiate reaction taken into account. The technique has no constraints concerning adiabatic or isothermal conditions hut is severely limited if the amount of reactants are small and/or the heat evolved is small. It is also not particularly suitable for intermetallic compounds where combustion is not part of the process during its formation. Its main use is in materials thermochemistry where it has been used in the determination of enthalpies of formation of carbides, borides, nitrides, etc. [Pg.82]

What are the main error sources in PAC experiments One of them may result from the calibration procedure. As happens with any comparative technique, the conditions of the calibration and experiment must be exactly the same or, more realistically, as similar as possible. As mentioned before, the calibration constant depends on the design of the calorimeter (its geometry and the operational parameters of its instruments) and on the thermoelastic properties of the solution, as shown by equation 13.5. The design of the calorimeter will normally remain constant between experiments. Regarding the adiabatic expansion coefficient (/), in most cases the solutions used are very dilute, so the thermoelastic properties of the solution will barely be affected by the small amount of solute present in both the calibration and experiment. The relevant thermoelastic properties will thus be those of the solvent. There are, however, a number of important applications where higher concentrations of one or more solutes have to be used. This happens, for instance, in studies of substituted phenol compounds, where one solute is a photoreactive radical precursor and the other is the phenolic substrate [297]. To meet the time constraint imposed by the transducer, the phenolic [Pg.201]

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